K-th Smallest XOR Value — Solution & Editorial

Back to the Problem

Reduce the linear basis to canonical form (each pivot bit isolated). The 2^rank distinct values are then in bijection with rank-bit numbers ordered by magnitude: the K−1 binary mask selects basis vectors.

Complexity: O(N · bits + rank²)

Watch out: Whether 0 counts as achievable when the basis is smaller than N (a dependency exists) shifts the entire ranking.